Ray Matrix Calculator

Build optical systems element by element. Compute the system ABCD matrix, effective focal length, back and front focal distances, and trace rays through the system.

Optical System
Element Stack (light order)1/10
1.
mm
[1.0000, 0] [-0.0100, 1.0000]
System Matrix
A = 1.00000B = 0
C = -0.010000D = 1.00000
Determinant (AD − BC)
Should equal n_in/n_out (1.0 for systems in air)
1.00000
System Properties
Effective focal length
EFL = −1/C
100.000mm
Back focal distance
BFD = −A/C (from last surface)
100.000mm
Front focal distance
FFD = D/C (from first surface)
-100.000mm
Abridged Optics — Ray Matrix Calculator v1.0Elements are applied in order from first to last (light travel direction). The system matrix is the product M_N × ... × M₂ × M₁.

All information, equations, and calculations have been compiled and verified to the best of our ability. For mission-critical applications, we recommend independent verification of all values. If you find an error, please let us know.